Association between CASP8-652 6N Del Polymorphism (rs3834129) and Colorectal Cancer Risk: Results from a Multi-Centric Study

The common 2652 6N del variant in the CASP8 promoter (rs3834129) has been described as a putative low-penetrance risk factor for different cancer types. In particular, some studies suggested that the deleted allele (del) was inversely associated with CRC risk while other analyses failed to confirm this. Hence, to better understand the role of this variant in the risk of developing CRC, we performed a multi-centric case-control study. In the study, the variant 2652 6N del was genotyped in a total of 6,733 CRC cases and 7,576 controls recruited by six different centers located in Spain, Italy, USA, England, Czech Republic and the Netherlands collaborating to the international consortium COGENT (COlorectal cancer GENeTics). Our analysis indicated that rs3834129 was not associated with CRC risk in the full data set. However, the del allele was under-represented in one set of cases with a family history of CRC (per allele model OR = 0.79, 95% CI = 0.69-0.90) suggesting this allele might be a protective factor versus familial CRC. Since this multi-centric case-control study was performed on a very large sample size, it provided robust clarification of the effect of rs3834129 on the risk of developing CRC in Caucasians.

Detailed experimental iced-storage characteristics of Barents Sea cod (Gadus morhua)

Im August 1997 wurde an Bord des FFS „Walther Herwig“ ein Eislagerversuch mit Kabeljau aus der Barebtssee durchgeführt. Die Fische wurden in täglichem Abstand auf ihre chemischen, physikalischen, sensorischen und mikrobiologischen Eigenschaften hin untersucht. Die analytischen Daten wurden jeweils mit den Tagen in Eis korreliert. Es erwies sich, daß die Werte vom Fischtester VI sowie RT Frischetester, von Dimethylamin- und Trimethylaminoxidstickstoff, die Qualitätseinstufung anhand des EUQualitätsbewertungsschemas, die sensorische Bewertung von gegarten Filetproben und die Gesamtkeimzahl auf der Haut am besten mit den im Eis verbrachten Tagen korrelierten. Die guteKorrelation zwischen sensorischen und instrumentell ermittelten Daten läßt in gewissem Umfang einen Ersatz von Sensorikdaten durch instrumentell ermittelten zu.

Measuring Learning Outcomes in Library Instruction

The author uses clicker technology to incorporate polling and multiple choice question techniques into library instruction classes. Clickers can be used to give a keener understanding of how many students grasp the concepts presented in a specific class session. Typically, a student that aces a definition-type question will fail to answer an application-type question correctly. Immediate, electronic feedback helps to calibrate teaching approaches and gather data about learning outcomes. This presentation will analyze learning outcomes specific to scientific disciplines, and demonstrate the usefulness of clickers to engage and sustain student learning.

The effect of traditional handling, processing and storage methods on the quality of dried fish in small scale fisheries in Nigeria

Most of the fish marketed throughout Nigeria are in either smoked or dried form. The technological requirement for other forms of preservation like chilling and freezing cannot be afforded by the small scale fisher folk. Considerable quantities of fish processed for distant consumer markets are lost at handling, processing, storage and marketing stages. Significant losses occur through infestation by mites, insects, fungal infestation and fragmentation during transportation. This paper attempts to describe the effect of these losses on fish quality and suggests methods of protecting fish from agents of deterioration

Storage potential and utilization of tilapia mince

Production of mince from Tilapia using a combination of physical and chemical methods was found to improve the storage life of the mince in the deep freezer. Though the chemical composition of the mince was slightly affected, the mince was microbiologically stable throughout the five weeks frozen storage. Fish cakes prepared traditionally from tilapia minces were more acceptable than oven dried cakes. Production of fish cakes form tilapia will improve utilization of this species in areas where small size tilapia are regarded as fish of low economic value

A preliminary investigation into the effect of different storage methods on the keeping quality of smoked Oreochromis niloticus

The study was carried out to asses the nutritional qualities of smoked O. niloticus and to discover the best methods of storage to minimize spoilage and infestation of smoked fish. Result showed that the protein contents in A and D decreased while the protein contents of b and C increased. The lipid content increased only in A while it decreased in B-C and D. The moisture content generally increased over the period of storage and there was an increase in ash content only in C while it decreased in A, B and D. The samples packed in polythene bag suffered about 35% mould infection and a few were attached by rodents with some fouling. Samples packed in jute bag were in good condition but were slightly attached by insect. All samples packed in carton and basket were still in good state but there were insect attack in those packed in carton

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Analog VLSI-based, neuromorphic sensorimotor systems: modeling the primate oculomotor system

Using neuromorphic analog VLSI techniques for modeling large neural systems has several advantages over software techniques. By designing massively-parallel analog circuit arrays which are ubiquitous in neural systems, analog VLSI models are extremely fast, particularly when local interactions are important in the computation. While analog VLSI circuits are not as flexible as software methods, the constraints posed by this approach are often very similar to the constraints faced by biological systems. As a result, these constraints can offer many insights into the solutions found by evolution. This dissertation describes a hardware modeling effort to mimic the primate oculomotor system which requires both fast sensory processing and fast motor control. A one-dimensional hardware model of the primate eye has been built which simulates the physical dynamics of the biological system. It is driven by analog VLSI circuits mimicking brainstem and cortical circuits that control eye movements. In this framework, a visually-triggered saccadic system is demonstrated which generates averaging saccades. In addition, an auditory localization system, based on the neural circuits of the barn owl, is used to trigger saccades to acoustic targets in parallel with visual targets. Two different types of learning are also demonstrated on the saccadic system using floating-gate technology allowing the non-volatile storage of analog parameters directly on the chip. Finally, a model of visual attention is used to select and track moving targets against textured backgrounds, driving both saccadic and smooth pursuit eye movements to maintain the image of the target in the center of the field of view. This system represents one of the few efforts in this field to integrate both neuromorphic sensory processing and motor control in a closed-loop fashion.

The Role of Fucose in Learning and Memory: The Identification of a Fucosylprotein, Synapsin I, in the Rat Brain and the Characterization of its Fucosylation

Previous studies have shown that the glycoproteins containing the fucose moiety are involved in neuronal communication phenomena such as long-term potentiation and memory formation. These results imply that fucose containing glycoproteins might play an important role in learning and memory. To understand the role of fucose in neuronal communication, and the mechanisms by which fucose may be involved in information storage, the identification of fucosylproteins is essential. This report describes the identification and characterization of fucosylproteins in the brain, which will provide new insights into the role of the fucose involved molecular interactions.

Cytokine control of neuronal phenotype

Diffusible proteins regulate neural development at a variety of stages. Using a novel neuronal culture assay, I have identified several cytokines that regulate the expression of neurotransmitters and neuropeptides in sympathetic neurons. These cytokines fall into two families. The first group is termed the neuropoietic cytokines, while including CDF/LIF, CNTF, OSM and GPA, induces expression of the same set of neuropeptide mRNAs in cultured sympathetic neurons. These four factors not only exhibit similar biological activities; they also share a predicted secondary structure and bind to a signal-transducing receptor subunit in common with IL-6 and IL-11. The latter two cytokines display a weaker activity in this assay. In addition, I find that several members of the TGF-β superfamily, activin A, BMP-2, and BMP-6, have a selective overlap with the neuropoietic family in the spectrum of neuropeptides that these cytokines induce in sympathetic neurons. Different patterns of neuropeptides induced by the TGF-β family members, however, demonstrate that the activities of these cytokines are distinct from those of the neuropoietic family. Another 30 cytokines are without detectable effect in this neuronal assay.

Activin A induces a set of neurotransmitters and neuropeptides that is somewhat similar to the phenotype of sympathetic neurons innervating sweat glands in rat footpads. In situ hybridization and RNase protection were carried out to test whether activins were involved in the phenotypic transition when sympathetic neurons contact sweat glands. I find that activin mRNA is present in both cholinergic and noradrenergic targets. Moreover, homogenates of footpads do not contain activin-like activity in the neuronal assay in vitro. Taken together, these data do not support activins as the best candidates for the sweat gland factor.

Several novel factors that regulate neuropeptide expression exist in heart cell conditioned medium. I attempted to purify these factors in collaboration with Dr. Jane Talvenheimo. Our results suggest that these factors are sensitive to the storage conditions used. Several modifications of purification strategy are discussed.

Structural and mechanistic study of monoalkyl diazenes. Synthesis, characterization, and reactivity of 1,6-didehydro[10]annulene

Methodology for the preparation of allenes from propargylic hydrazine precursors under mild conditions is described. Oxidation of the propargylic hydrazines, which can be readily prepared from propargylic alcohols, with either of two azo oxidants, diethyl azodicarboxylate (DEAD) or 4-methyl 1,2-triazoline-3,5-dione (MTAD), effects conversion to the allenes, presumably via sigmatropic rearrangement of a monoalkyl diazene intermediate. This rearrangement is demonstrated to proceed with essentially complete stereospecificity. The application of this methodology to the preparation of other allenes, including two that are notable for their reactivity and thermal instability, is also described.

The structural and mechanistic study of a monoalkyl diazene intermediate in the oxidative transformation of propargylic hydrazines to allenes is described. The use of long-range heteronuclear NMR coupling constants for assigning monoalkyl diazene stereochemistry (E vs Z) is also discussed. Evidence is presented that all known monoalkyl diazenes are the E isomers, and the erroneous assignment of stereochemistry in the previous report of the preparation of (Z)-phenyldiazene is discussed.

The synthesis, characterization, and reactivity of 1,6-didehydro[10]annulene are described. This molecule has been recognized as an interesting synthetic target for over 40 years and represents the intersection of two sets of extensively studied molecules: nonbenzenoid aromatic compounds and molecules containing sterically compressed π-systems.The formation of 1,5-dehydronaphthalene from 1 ,6-didehydro[10]annulene is believed to be the prototype for cycloaromatizations that produce 1,4-dehydroaromatic species with the radical centers disposed anti about the newly formed single bond. The aromaticity of this annulene and the facility of its cycloaromatization are also analyzed.

The electrocatalytic and stoichiometric oxidation chemistry of binuclear ruthenium complexes incorporating the anionic tripod ligand {(η5-C5H5)Co[P(OCH3)2(=O)]3}-

The anionic tripod ligand NaLoMe (L_(oMe) - = [(η^5-C_5H_5)Co{P(O)(OCH_3)_2}_3]^-) reacts with RuO_4 in a biphasic reaction mixture of 1% H_2SO_4 and CCI_4 to afford [(L_(oMe) (HO)Ru^(IV) (µ-O)_2Ru ^(IV)(OH)(L_(oMe)] (1), which is treated with aqueous CF_3S0_3H to generate [(L_(oMe)(H_2O)Ru^(IV) (µ-O)_2R^(IV) (OH_2)(L_(oMe)][CF_3SO_3]_2 ([H_21][CF_3SO_3]_2). Addition of iodosobenzene to an acetonitrile solution of this salt yields [(L_(oMe)(O)Ru^v(µ-0)2Ru^v-(O)(_(LoMe)] (2). The dimer 1 can be reduced chemically or electrochemically to the Ru^(III)- Ru^(III) dimers [(L_(oMe)(H_20)Ru^(III) (µ-OH)_2Ru^(III) (OH_2)(L_(oMe)) ]^2+ and [(L_(oMe)) ^(III) (µ-0Hh(µ-0H2)Ru^(III) (L_(oMe)]^2+ which interconvert in aqueous media. Two electron processes dominate both the bulk chemistry and the electrochemistry of 1. Among these processes are the quasi-reversible Ru^(IV) - Ru^(IV)/Ru^(III)- Ru^(III) and Ru^(III)- Ru^(III)/ Ru^(II)- Ru^(II) reductions and a largely irreversible Ru^(V) - Ru^(V)/ Ru^(IV) - Ru^(IV)/oxidation. The dioxo dimer 2 oxidizes alcohols and aldehydes in organic media to afford 1 and the corresponding aldehydes and acids. Analogously, the Ru^(V) - Ru^(V)/ Ru^(IV)- Ru^(IV) redox wave mediates the electrooxidation of alcohols and aldehydes in aqueous buffer. In this system, substrates can be oxidized completely to CO_2. The kinetic behavior of these oxidations was examined by UV-vis and chronoamperometry, respectively, and the chemistry is typical of metal-oxo complexes, indicating that electronic coupling between two metal centers does not dramatically affect the metal-oxo chemistry. Dimer [H_21]^(2+) also reacts with alcohols, aldehydes, and triphenylphosphine in CH_3CN to afford Ru^(III)- Ru^(III) products including [(L_(oMe))CH_3CN) Ru^(III) (µ-OH)_2 Ru^(III) (NCCH_3)( L_(oMe))][CF_3SO_3]2 (characterized by X-ray crystallography) and the corresponding organic products. Reaction of 1 with formaldehyde in aqueous buffer quantitatively affords the triply bridged dimer [(L_(oMe)Ru^(III) (µ-OH)2- (µ-HCOO) Ru^(III) (L_(oMe)][CF_3SO_3] (characterized by X-ray crystallography). This reaction evidently proceeds by two parallel inner-sphere pathways, one of which is autocatalytic. Neither pathway exhibits a primary isotope effect suggesting the rate determining process could be the formation of an intermediate, perhaps a Ru^(IV) - Ru^(IV) formate adduct. The Ru^(III)- Ru^(III)formate adduct is easily oxidized to the Ru^(IV) - Ru^(IV) analog [(L_(oMe)Ru^(IV)(µ-OH)_2-(µ-HCOO) Ru^(IV) (L_(oMe)][CF_3SO_3], which, after isolation, reacts slowly with aqueous formaldehyde to generate free formate and the Ru^(III)- Ru^(III) formate adduct. These dimers function as catalysts for the electrooxidation of formaldehyde at low anodic potentials (+0.0 V versus SCE in aqueous buffer, pH 8.5) and enhance the activity of Nafion treated palladium/carbon heterogeneous fuel cell catalysts.

Synthesis, structure, and photophysics of polypyridophenazine transition-metal complexes

The condensation of phenanthroline-5,6-dione (phendione) with polyamines is a versatile synthetic route to a wide variety of chelating ligands. Condensation with 2,3- napthalene diamine gives benzo[i]dipyrido[3,2-a:2',3'-c]phenazine (bdppz) a ligand containing weakly-coupled orbitals of benzophenazine (bpz) and 2,2' -bipyridinde(bpy) character. The bpy character gives Re and Ru complexes excited-state redox properties; intramolecular electron transfer (ET) takes place to the bpz portion of the ligand. The charge-separated state so produced has an extraordinarily-long 50 µs lifetime. The slow rate of charge recombination arises from a combination of extremely weak coupling between the metal center and the bpz acceptor orbital and Marcus "inverted region" behavior. Molecular orbital calculations show that only 3% the electron density in the lowest unoccupied molecular orbital lies on the bpy atoms of bdppz, effectively trapping the transferred electron on the bpz portion. The rate of charge recombination decreases with increasing driving force, showing that these rates lie in the inverted region. Comparison of forward and back ET rates shows that donor-acceptor coupling is four orders of magnitude greater for photoinduced electron transfer than it is for thermal charge recombination.

Condensation of phendione with itself or tetramines gives a series of binucleating tetrapyridophenazine ligands of incrementally-varying coordination-site separation. When a photoredox-active metal center is attached, excited-state energy and electron transfer to an acceptor metal center at the other coordination site can be studied as a function of distance. A variety of monometallic and homo- and heterodimetallic tetrapyridophenazine complexes has been synthesized. Electro- and magnetochemistry show that no ground-state interaction exists between the metals in bimetallic complexes. Excited-state energy and electron transfer, however, takes place at rates which are invariant with increasing donor-acceptor separation, indicating that a very efficient coupling mechanism is at work. Theory and experiment have suggested that such behavior might exist in extended π-systems like those presented by these ligands.

Condensation of three equivalents of 4,5-dimethyl-1,2-phenylenediamine with hexaketocyclohexane gives the trinucleating ligand hexaazahexamethyltrinapthalene (hhtn). Attaching two photredox-active metal centers and a third catalytic center to hhtn provides means by which multielectron photocatalyzed reactions might be carried out. The coordination properties of hhtn have been examined; X-ray crystallographic structure determination shows that the ligand's constricted coordination pocket leads to distorted geometries in its mono- and dimetallic derivatives.

Effect of locally available spices on the organoleptic and storage periods of Heterotis niloticus

Investigation were carried out on the effect of some locally available species in the enhancement of the organoleptic quality and the storage periods of smoked Heterotis niloticus using Pprosopis africana as common smoke sources. Samples of fresh H. niloticus were bought, cut into chunks while extract juice from pepper, ginger rhizomes, garlic, onion bulb were used as sources of spices. Samples of fish were divided randomly into five (5) batches dipped into spice extract juices for 10 minutes drained and smoked with common firewood. Treatment without spice extract juice served as control. Each batch of fish was smoked for 7 hours on a drum-made smoking kiln products were individually packaged in polythene bag stored at room temperature and used for sensory evaluation and microbial analysis. Results of the sensory evaluation indicated that there was significant difference (P<0.005) for taste, appearance, colour and overall acceptance for the treatments. Ginger juice extract had the best overall acceptance. Similarly there was significant difference (P>0.05) in the microbial analysis. The garlic juice extract had the longest storage period with minimum total plate and mould count after 8 weeks

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.