Strong evidence for a novel schizophrenia risk locus on chromosome 1p31.1 in homogeneous pedigrees from Tamil Nadu, India

OBJECTIVE: The study of ethnically homogeneous populations may help to identify schizophrenia risk loci. The authors conducted a genomewide linkage scan for schizophrenia in an Indian population. METHOD: Participants were 441 individuals (262 affected probands and siblings) who were recruited primarily from one ethnically homogeneous group, the Tamil Brahmin caste, although individuals from other geographically proximal castes also participated. Genotyping of 124 affected sibling pair pedigrees was performed with 402 short tandem repeat polymorphisms. Linkage analyses were conducted using nonparametric exponential LOD (logarithm of the odds ratio for linkage) scores and parametric heterogeneity LOD scores. Parametric heterogeneity scores were calculated using simple dominant and recessive models, correcting for multiple statistics. The data were examined for evidence of consanguinity. Genomewide significance levels were determined using 10,000 gene dropping simulations. RESULTS: These findings revealed genomewide significant linkage to chromosome 1p31.1, through the use of both exponential and heterogeneity LOD scores, incorporating correction for multiple statistics and mild consanguinity. The estimated sibling recurrence risk associated with this putative locus was 1.95. Analysis for heterogeneity LOD scores also detected suggestive linkage to chromosomes 13q22.1 and 16q12.2. Using 117 tag single nucleotide polymorphisms (SNPs), family-based association analyses of phosphodiesterase 4B (PDE4B), the closest schizophrenia candidate gene, detected no convincing evidence of association, suggesting that the chromosome 1 peak represents a novel risk locus. CONCLUSIONS: This is the first study-to the authors' knowledge-to report significant linkage of schizophrenia to chromosome 1p31.1. Further investigation of this chromosome region in diverse populations is warranted to identify underlying sequence variants.

A dual-slope analogue-to-digital converter for generating polynomials

A new digital polynomial generator using the principle of dual-slope analogue-to-digital conversion is proposed. Techniques for realizing a wide range of integer as well as fractional coefficients to obtain the desired polynomial have been discussed. The suitability of realizing the proposed polynomial generator in integrated circuit form is also indicated.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Homogeneous hydrogenations ofα, β-unsaturated compounds using pentacyanocobaltate (II) anion as catalyst system

Hydrogenation of someα, β-unsaturated carbonyl compounds using potassium pentacyanocobaltate (II), K3Co(CN)5, as a homogeneous catalyst has been investigated. Thus, hydrogenation of 1-carvone (I), mesityl oxide (4), 2-cyclohexenone (8) and benzalacetone (6) afforded the corresponding dihydrocompounds. Hydrogenation ofβ-ionone (10) afforded a mixture of theα, β-dihydrocompounds (14) and (15). In all these cases, it was observed that the reaction proceeded to completion only in the presence of added base. Hydrogenation of 5α-androst-l-en-17β-ol-3-one acetate (19) afforded the saturated compound, 5α-androst-17β-ol-3-one (20) in 60% yield. It was found that other steroid enones and dienones were not reduced by this catalyst system.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Experiments on homogeneous nucleation and physicochemical properties related to atmospheric new particle formation

Aerosol particles play a role in the earth ecosystem and affect human health. A significant pathway of producing aerosol particles in the atmosphere is new particle formation, where condensable vapours nucleate and these newly formed clusters grow by condensation and coagulation. However, this phenomenon is still not fully understood. This thesis brings an insight to new particle formation from an experimental point of view. Laboratory experiments were conducted both on the nucleation process and physicochemical properties related to new particle formation. Nucleation rate measurements are used to test nucleation theories. These theories, in turn, are used to predict nucleation rates in atmospheric conditions. However, the nucleation rate measurements have proven quite difficult to conduct, as different devices can yield nucleation rates with differences of several orders of magnitude for the same substances. In this thesis, work has been done to have a greater understanding in nucleation measurements, especially those conducted in a laminar flow diffusion chamber. Systematic studies of nucleation were also made for future verification of nucleation theories. Surface tensions and densities of substances related to atmospheric new particle formation were measured. Ternary sulphuric acid + ammonia + water is a proposed candidate to participate in atmospheric nucleation. Surface tensions of an alternative candidate to nucleate in boreal forest areas, sulphuric acid + dimethylamine + water, were also measured. Binary compounds, consisting of organic acids + water are possible candidates to participate in the early growth of freshly nucleated particles. All the measured surface tensions and densities were fitted with equations, thermodynamically consistent if possible, to be easily applied to atmospheric model calculations of nucleation and subsequent evolution of particle size.

On the homogeneous and heterogeneous nucleation of some organic compounds

The conversion of a metastable phase into a thermodynamically stable phase takes place via the formation of clusters. Clusters of different sizes are formed spontaneously within the metastable mother phase, but only those larger than a certain size, called the critical size, will end up growing into a new phase. There are two types of nucleation: homogeneous, where the clusters appear in a uniform phase, and heterogeneous, when pre-existing surfaces are available and clusters form on them. The nucleation of aerosol particles from gas-phase molecules is connected not only with inorganic compounds, but also with nonvolatile organic substances found in atmosphere. The question is which ones of the myriad of organic species have the right properties and are able to participate in nucleation phenomena. This thesis discusses both homogeneous and heterogeneous nucleation, having as theoretical tool the classical nucleation theory (CNT) based on thermodynamics. Different classes of organics are investigated. The members of the first class are four dicarboxylic acids (succinic, glutaric, malonic and adipic). They can be found in both the gas and particulate phases, and represent good candidates for the aerosol formation due to their low vapor pressure and solubility. Their influence on the nucleation process has not been largely investigated in the literature and it is not fully established. The accuracy of the CNT predictions for binary water-dicarboxylic acid systems depends significantly on the good knowledge of the thermophysical properties of the organics and their aqueous solutions. A large part of the thesis is dedicated to this issue. We have shown that homogeneous and heterogeneous nucleation of succinic, glutaric and malonic acids in combination with water is unlikely to happen in atmospheric conditions. However, it seems that adipic acid could participate in the nucleation process in conditions occurring in the upper troposphere. The second class of organics is represented by n-nonane and n-propanol. Their thermophysical properties are well established, and experiments on these substances have been performed. The experimental data of binary homogeneous and heterogeneous nucleation have been compared with the theoretical predictions. Although the n-nonane - n-propanol mixture is far from being ideal, CNT seems to behave fairly well, especially when calculating the cluster composition. In the case of heterogeneous nucleation, it has been found that better characterization of the substrate - liquid interaction by means of line tension and microscopic contact angle leads to a significant improvement of the CNT prediction. Unfortunately, this can not be achieved without well defined experimental data.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Hydrolytic reactions of tetrasulphur tetranitride in a homogeneous medium

The hydrolytic reactions of tetrasulphur tetranitride are studied in a homogeneous medium. Alkaline hydrolysis gives sulphite, thiosulphate, sulphate and sulphide whereas the products in acid hydrolysis are mainly sulphur dioxide, elemental sulphur and hydrogen sulphide, with traces of polythionates. Under optimum conditions, tetrasulphur tetranitride reacts with sulphite consuming 2 moles of sulphite per mole of sulphur nitride to give 2 moles of trithionate. The reaction of sulphur nitride with thiosulphuric acid gives pentathionate and tetrathionate.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Hydrolytic reactions of esters and amides of thiosulphurous acid in a homogeneous medium

The hydrolytic reactions of esters and amides of thiosulphurous acid are investigated in a homogeneous medium. The esters are hydrolysed by alkali to give sulphide, sulphite and thiosulphate whereas the amides are resistant towards alkali. Both the esters and amides are hydrolysed by acids giving hydrogen sulphide, sulphur dioxide, polythionates and elemental sulphur. The hydrolysis of these esters and amides in presence of sulphurous acid and thiosulphuric acid gives tetrathionate and hexathionate, respectively.